The conventional twelve coin balancing puzzle involves the provision of twelve identically appearing coins. One of these coins is a counterfeit and differs from the other coins only in its weight. This counterfeit coin can be either slightly lighter or slightly heavier than the other eleven coins. The puzzle is to determine, by means of a balance scale, which of the twelve coins is the counterfeit and whether it is lighter or heavier with only three weighings. The mathematician Gauss proved that such could be accomplished.
It will be appreciated from the foregoing that once a person has worked the puzzle successfully, he is then aware that the counterfeit coin is either lighter or heavier. Knowing this information, he cannot again mix up the coins and attempt to repeat the puzzle since his foreknowledge that the counterfeit coin is either lighter or heavier has already provided him with part of the answer. It would be desirable if a puzzle could be provided of the foregoing type wherein a player could start to solve the puzzle in every instance without previous knowledge as to whether the counterfeit coin is lighter or heavier.